Prime and Composite Numbers — Let's Practise!

Prime and Composite Numbers — Let's Practise! exercise

• What are prime and composite numbers?

  Hints

  Use the examples below to help you answer the questions.

  9 is a composite number. Its factors are 1, 3, and 9:

  • 1 x 9
  • 3 x 3

  3 is a prime number. Its factors are 1 and 3:

  • 1 x 3

  Make a list with all the factors of 12 and 7.

  The prime number will have fewer factors than the composite number.

  Solution

  1. A prime number has only two factors - 1 and itself.
  2. A composite number has more than two factors.
  3. 12 is a composite number.

  • 12 is composite because it has more than 2 factors: 1, 2, 3, 4, 6 and 12.

  4. 7 is a prime number.

  • 7 is prime because it has only 2 factors: 1 and 7 (itself).

• Say whether 45 is prime or composite by listing all factors.

  Hints

  Let's do one together.

  3 is a factor of 45. How many times does 3 go into 45?

  3 goes into 45 15 times. So, 15 is a factor of 45.

  Remember, a number is prime when it has only 2 factors: 1 and itself.

  How many factors did you find for 45?

  Solution

  The factor pairs of 45 are:

  • 1 x 45
  • 3 x 15
  • 5 x 9

  45 is composite.

• Answer the questions and fill in the missing factors.

  Hints

  Let's complete the factor pair 3 x ? = 99.

  First, find out how many times 3 goes into 99.

  3 goes into 99 33 times. So, 33 is the missing factor in the pair.

  Can you find the other factors?

  A prime number has only two factors: 1 and itself.

  A composite number has more than two factors.

  Apply these rules to the factors you found for 83, 99 and 63.

  Solution

  83: There are 2 factors, 1 and 83.

  99: The factor pairs of 99 are:

  • 1 x 99
  • 3 x 33
  • 9 x 11.

  63: The factor pairs of 63 are:

  • 1 x 63
  • 3 x 21
  • 7 x 9.

  The prime number in the image is: 83.

  The composite numbers in the image are: 99 and 63.

• Help Razzi find all the factors for the numbers below.

  Hints

  Start by finding all the factor pairs of 65. Can you fill in the missing factors?

  1 x ?

  5 x ?

  Let's list the factor pairs of 52. Can you find the missing factors?

  1 x 52

  ? x 26

  4 x ?

  For the last three gaps, use the numbers 65, 67 and 52.

  Solution

  65

  • The factors of 65 are: 1, 5, 13, 65

  67

  • The factors are: 1 and 67

  52

  • The factors are: 1, 2, 4, 13, 26, 52

  The prime number is 67.

  The composite numbers are 52 and 65.

• Answer the questions about the numbers 17 and 16.

  Hints

  Let's find the missing factor in the pair ? x 8 = 16.

  Here, 16 has been split up into groups of 8, how many groups are there?

  There are 2 groups of 8 in the image so 2 x 8 is a factor pair of 16.

  Remember:

  You can check if a number is prime or composite by how many factors it has.

  If it has more factors than 1 and itself, it's composite.

  Solution

  The factor pairs of 17 are: 1 x 17.

  17 is prime.

  The factor pairs of 16 are:

  1 x 16

  2 x 8

  4 x 4

  16 is composite.

• What are the prime numbers between 30 and 40?

  Hints

  Remember, a prime number only has two factors: 1 and itself.

  Let's find the factors of 32 together.

  The factor pairs of 32 are: 1 x 32, 2 x 16, 4 x 8. There are six factors.

  So, 32 cannot be prime because it has more factors than just 1 and itself.

  Remember, if a number has more than 2 factors it must be composite.

  The even numbers between 30 and 40 cannot be prime because they have 2 as a factor!

  Solution

  The prime numbers between 30 and 40 are: 31 and 37.